Fiber-reinforced polymers (FRPs) are materials that comprise high-strength continuous fibers and resin polymer, and the resins comprise a matrix in which the fibers are embedded. As the technique of FRP production has advanced, FRPs have attained many incomparable advantages over traditional building materials such as concrete and steel, and thus they play a significant role in the strengthening and retrofitting of concrete structures. Bridges that are built out of FRPs have been widely used in overpasses of highways, railways and streets. However, damages in FRP bridges are inevitable due to long-term static and dynamic loads. The health of these bridges is important. Here, we review the maintenance and inspection methods for FRP structures of bridges and analyze the advantages, shortcomings and costs of these methods. The results show that two categories of methods should be used sequentially. First, simple methods such as visual inspection, knock and dragging-chain methods are used to determine the potential damage, and then radiation, modal analysis and load experiments are used to determine the damage mode and degree. The application of FRP is far beyond the refurbishment, consolidation and construction of bridges, and these methods should be effective to maintain and inspect the other FRP structures.